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Particularly the 'Apply' sections at the end of the worksheets.

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Angles: compass directions Video 27b Practice Questions

Area: quarter-circle Video 47a Practice Questions

Averages: combined mean Video 53a Practice Questions Textbook Exercise

Averages: mode (frequency table) Video 56a

Averages: range (frequency tables) Video 57a

Averages: Quartiles Video 57b Practice Questions

Circles: perimeter - quarter-circle Video 62a Practice Questions

Circle theorems proof: right angle in a semi-circle Video 65a Practice Questions

Circle theorems proof: angles at circumference\centre Video 65b Practice Questions

Circle theorems proof: angles in the same segment Video 65c Practice Questions

Circle theorems proof: cyclic quadrilaterals Video 65d Practice Questions

Circle theorems proof: alternate segment theorem Video 65e Practice Questions

Circle theorems proof: radius and tangent proof Video 65f Practice Questions

Circle theorems proof: Textbook Exercise

Constructions: loci part 3 Video 77 Practice Questions Textbook Exercise

Coordinates: 3D Video 86 Practice Questions

Data handling cycle Video 89 Practice Questions

Dimensional analysis Video 97 Practice Questions

Division: long division Video 98a

Enlargements: ray method Video 109 Practice Questions

Equations: involving fractions Video 111 Practice Questions Textbook Exercise

Equations: x squared Video 116a Practice Questions

Equations: Think of a number Video 116b Practice Questions

Factorisation: splitting the middle Video 119a Textbook Exercise

Factorisation: difference of 2 squares Video 120 Practice Questions Textbook Exercise

Fractions: finding the midpoint Video 141a Practice Questions

Graphs composite bar charts Video 148a

Graphs: dual bar charts Video 148b

Graphs: misleading graphs Video 160a

Graphs: real life linear graphs Video 171a

Linear graphs: real life Video 198a

Money - See Video 400 or click here for collection

Multiplication: grid method Video 199 Practice Questions Textbook 1 Textbook 2

Multiplication: column method Video 200 Practice Questions Textbook 1 Textbook 2

Multiplication: times tables Video 204a Textbook Exercise

Number: odd and even numbers Video 221a Practice Questions

Number: product of primes (squares/cubes) Video 223a Practice Questions Textbook

Percentages: simple interest Video 236a Practice Questions Textbook Exercise

Proportion: unitary method Video 255a Practice Questions Textbook Exercise

Proportion: Graphs Video 255b

Proportion: Time Video 255c

Pythagoras: area of a regular hexagon Video 262 Practice Questions

Quadratic graphs: sketching using key points Video 265 Textbook Exercise

Quadratic graphs: finding turning point Video 265a Practice Questions

Quadratic graphs: line of symmetry Video 265b

Quadratics: solving (factorising) Video 266 Practice Questions Textbook 1 Textbook 2

Quadratics: solving graphically Video 267c Practice Questions Textbook Exercise

Quadratics: solving graphically advanced Video 267d Practice Questions

Questionnaires Video 268 Practice Questions

Ratio: express as fractions or % Video 269a Practice Questions Textbook Exercise

Ratio: given two ratios Video 271a Textbook Exercise

Ratio: difference between Video 271b Textbook Exercise

Ratio: expressing as 1:n Video 271c Textbook Exercise

Ratio: equations/ratios Video 271d

Ratio: solving problems 1 Video 271e Textbook Exercise

Sampling: using samples Video 281a

Sampling: random Video 282 Practice Questions

Scales and maps Video 283 Practice Questions

Sequences: nth term for fractional sequences Video 289 Textbook Exercise

Similar shapes: definition Video 291 Practice Questions

Similar shapes: further Video 294 Practice Questions

Simultaneous equations (substitution, both linear) Video 296 Practice Questions

Simultaneous equations (graphical) Video 297 Textbook Exercise

Surface area: mixture Video 309 Practice Questions

Surface area: other prisms Video 312

Transformations: mixture Practice Questions

Transformations of graphs Video 323 Practice Questions

Transformations of trigonometric graphs Video 324 Practice Questions

Trigonometry: sine rule (ambiguous case) Video 334a Textbook Exercise

Trigonometry: area of a triangle Video 337 Proof Practice Questions Textbook Exercise

Types of data: primary & secondary Video 343a Practice Questions Textbook Exercise

Types of graph: cubics Video 344 Practice Questions

Types of graph: exponential Video 345 Practice Questions

Types of graph: reciprocal Video 346 Practice Questions

Types of graph: mixture

Units: types of metric and imperial unit Video 347 Practice Questions

Units: Converting imperial units for length Video 348a Practice Questions

Units: Converting imperial units for mass Video 348b Practice Questions

Units: Converting imperial units for capacity Video 348c Practice Questions

Units: metric to imperial (length) Video 349d Practice Questions

Units: metric to imperial (mass) Video 349e Practice Questions

Units: metric to imperial (capacity) Video 349f Practice Questions

Vectors Video 353 Practice Questions

Views: front/side elevation and plan view Video 354 Practice Questions

Volume: Frustum Video 360a Textbook Exercise

Additional Topics

Flow Charts Video 364 Practice Questions

Geometric Proof Video 366

Identities: Equating coefficients Video 367 Practice Questions

Identities, Formula, Equations etc Video 367a Practice Questions

Intersecting Chord Theorem Video 368a Practice Questions

Intersecting Secant Theorem Video 368b Practice Questions

Quadratic graph (completing the square) Video 371

Equation of a Tangent to a Circle Video 372 Practice Questions

Iteration Video 373 Practice Questions

Iterative Processes Video 373a

Change of Sign Video 373a Practice Questions

Arithmetic progressions Video 374

Geometric progressions Video 375

Set notation Video 379

Venn Diagrams Video 380 Practice Questions

Shortest distance from point to a line Video 381 Textbook Exercise

Time series Video 382

Population Density Video 384a Practice Questions

Invariant Points Video 392 Textbook Exercise

Simultaneous Equations (3 Unknowns) Video 393 Textbook Exercise

Measuring Lines Video 397 Practice Questions

Drawing Lines Video 397a Practice Questions

Money: Coins Video 400a Practice Questions

Money: Change Video 400b

Money: Buying Video 400c Practice Questions

Money: Regular Payments Video 400d Practice Questions

Money: Bills Video 400e

Money: Discounts Video 400f Practice Questions

Money: VAT Video 400g Practice Questions

Money: Wages Video 400h Practice Questions

Money: Bank Statements Video 400i Practice Questions

Money: Tax Video 400j Practice Questions

Money: Cost per kg Video 400k Practice Questions

Money: Cost per litre Video 400l Practice Questions

Money: Cost per metre Video 400m Practice Questions

Money: Reading meters Video 400n

Money: Profit Video 400p Practice Questions

Money: Greatest/Maximum Video 400q Practice Questions

Money: Estimation Video 400r Practice Questions

Money: Midpoint Video 400s Practice Questions

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Videos, Practice Questions and Textbook Exercises on every Secondary Maths topic

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Some nice lessons on here with well though out examples and sometimes non-examples.

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The cookie settings on this website are set to "allow cookies" to give you the best browsing experience possible. If you continue to use this website without changing your cookie settings or you click "Accept" below then you are consenting to this.

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This website is my attempt to assemble a collection of high-quality, sequences of questions and examples using key principles from Variation Theory. By holding key features between questions and examples constant, together with the mathematical behaviour that I call Reflect, Expect, Check, Explain and the supporting role of the teacher, I believe we can help students better understand key mathematical ideas.

You can find out more about the site and the different types of sequences available by visiting the Introduction.

You can access all the sequences of questions and examples from the Topics menu above.

My 2020 book, Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom, goes into detail about making the most of these activities in the classroom. You can order the book from Amazon, John Catt, or wherever you get your books.

My 2023 book, Tips for Teachers: 400+ ideas to improve your teaching, details my most recent thoughts on using these sequences effectively. You can order the book from Amazon, John Catt, or wherever you get your books.

I have an online course store which offers low-cost, high-quality CPD on-demand. Each course contains short videos, resources, research, activities and questions to reflect upon. The courses most suited to the sequencers on the Variation Theory website are:

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Sequences and behaviour to enable mathematical thinking in the classroom - by Craig Barton @mrbartonmaths

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The Corbettmaths 5-a-day for the 9-1 GCSE.

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Great for KS3.
The powerpoints for these are already downloaded on Woldgate's network.

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This is our main intervention that aims to increase the mental strategies, timestables and key skills fluency of KS3 students, preparing them for later KS4 study. The emphasis is on this being a regular, short exercise at the beginning of KS3 lessons lasting no more than 10 mins. There should be a sense of real pace to a well-conducted Ninja session!

Preparation

Decide how many sessions you will run Numeracy Ninjas each week. We advise every KS3 lesson for the first 10 weeks then adjusting accordingly.

Download the relevant Ninja Skill Books and print/photocopy one copy for each student. We've made these free to download; of course, you'll have to meet the costs of printing/photocopying!

Download the Numeracy Ninjas PowerPoint and make sure all teachers can access it.

Download the Numeracy Ninjas Record Spreadsheet and make sure all teachers can access it.

In-Class Delivery

The whole session should be completed within 10 mins. The emphasis is on this being regular, quick fluency practice, not on it becoming a whole lesson.

Open the Numeracy Ninjas Powerpoint, place it in Slideshow mode and click the link to the relevant week and session. Have this displayed as your students enter the room. They collect their Ninja Skill Book and open it to the relevant page, ready to begin.

When all students are ready, click to go to the next slide on the PowerPoint which will then say, click the logo to begin.

Click the logo and the 5 minute timer will start. You will see the circular belt badges fade out as the time progresses. Students complete as many questions from their Ninja Skill Books as they can during this time. The Mental Strategies and Timestables sections should be done mentally; they may use written calculations in the space provided for the questions.

Circulate whilst students are working on the task, gaining some AFL on which questions would be good to briefly discuss when students mark their answers.

Your time is up! will appear at the end of the 5 minutes. Students then get themselves ready to mark their answers.

Click through the next 3 slides on the PowerPoint reading out the answers whilst the students mark their work. Briefly discuss strategies with the class for particular questions that you picked up from your AFL.

Click to the next slide on the PowerPoint which will display the Ninja Score-Belt poster. Students add up their scores for each of the 3 sections and calculate their Ninja Score. They look up which colour they have achieved.

Finally, open the Numeracy Ninjas Record Spreadsheet and enter the students' scores into the relevant session as they read them out.

Collect in the Ninja Skill Books and carry on with teaching the syllabus!

Ongoing

Each half term award the highest performing and most improved students in each class Grand Master status. You can give them Grand Master certificates (available to download for free from the Promotional Materials page) or celebrate their success with prizes from our Online Shop.

Numeracy Ninja Skill Focus Worksheets

This is a suite of additional intervention materials which allow students to work on improving individual topics. There are 10 days of exercises in each Ninja Skill Focus Worksheet. Students complete the exercises each day, consecutively for 10 days. They may like to record the time it took to complete the exercises so they can see their progress.

For more information on how to run this intervention, and to download the Ninja Skill Focus Worksheets click here.

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This is our main intervention that aims to increase the mental strategies, timestables and key skills fluency of KS3 students, preparing them for later KS4 study. The emphasis is on this being a regular, short exercise at the beginning of KS3 lessons lasting no more than 10 mins.

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Great for introducing a concept - showing what it is and what it isn't.

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NonExamples.com - Something that is not an example of a rule or definition already shown, used for a clearer explanation.

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Maths Whiteboard - example-problem pairs

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Maths Whiteboard - example-problem pairs

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Great for picking out misconceptions and a quick way to judge a groups understanding.

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Don't spend hours marking books

Diagnostic Questions is a world leading assessment tool that provides detailed insights into student understanding in a fraction of the time, simultaneously reducing your workload and improving student results and confidence.

25,000 Questions & Quizzes

Create your own or choose from the thousands created by teachers, awarding bodies and publishers.

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Use our powerful Data Analytics, Feedback and Planning tools to understand your students better than ever.

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We're in the business of helping teachers. We know how tight departmental budgets are, we know the pain of change and we know how frustrating it is when a product you've come to depend upon starts charging. Well, we're giving you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free. It's a small gesture, but we hope it helps.

Supported Subjects

Expected in November 2016, the ultimate GCSE Computing companion, with Scheme of Work and 1000s of questions from OCR and teachers.

750 questions from the Royal Society of Chemistry plus 1000s of others from teachers across the UK covering, Biology, Chemistry and Physics.

We want to support the most popular subjects that you teach. Help us focus on subjects that will make a difference by voting for our next subject.

Resolving misconceptions improves performance

A continuous system of misconception identification provides teachers with the foresight they need to intervene effectively in students' learning.

"Good diagnostic questions encapsulate our best information about what students find difficult, and are an indispensable part of any teacher's repertoire."
Dr. Dylan Wiliam, Emeritus Professor of Educational Assessment @UCL

"...the single greatest step forward in AFL in the maths classroom for years. I think it would be hard to find any better AFL strategy out there."
William Emeny, greatmathsteachingideas.com

"...good questions help us know more about our students' learning and help us to address misconceptions. An outstanding new resource to help us do just that."
Colleen Young, colleenyoung.wordpress.com

"Discover key misconceptions before you teach, track progress, review students explanations and quickly give personalised feedback."
Mohammed Ladak, mathedup.co.uk

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Better results, more confidence, less time

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Since I started teaching three years ago, I've been well aware of the problems of traditional textbook exercises when introducing a class to a new concept, procedure. More often than not, textbook exercises became far too varied too quickly, with pupils becoming quickly unstuck, and it became difficult to identify the source of their confusion. Alternatively, it felt as though I was presenting students with 'just more practice of the same', which was deeply unsatisfactory (regardless of the prior attainment of the pupils).

Hence (and I am hugely indebted to Mr Barton and his book), creating sequences of intelligent, minimally varied practice questions seemed a reasonable step. When they are used to introduce pupils to a topic, they enable pupils to make connections and really focus on the underlying concept. The ones presented here are very much initial attempts - they are not a perfect model of how to write minimally varied exercises. All the same, I hope you find them of some use!

I am contactable at fortyninecubed (at) gmail . com, or on Twitter at @fortyninecubed.

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Since I started teaching three years ago, I've been well aware of the problems of traditional textbook exercises when introducing a class to a new concept, procedure. More often than not, textbook exercises became far too varied too quickly, with pupils becoming quickly unstuck, and it became difficult to identify the source of their confusion....

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In 2016, I attended #MathsConf7 in Leeds. The outcome? A to-do list longer than my arm as I intended to create a textbook of exercises of increasingly difficult questions to improve upon the standard textbook diet that we in the UK feed from. 's 'Best New Resources' ahead of EdExcel's materials to support the new GCSE.
Resourceaholic.com
In February 2020, Craig Barton announced me as 'the master of fluency practice' for these resources.
In April 2017, IDQs was announced as

In between these two times, I've had a promotion at work, a difficult time with a beloved family pet and a new arrival (Elizabeth Taylor, who is now 'not so new'), so time hasn't really been something that I've been accustomed to ...

... but I had turned my attention to randomising the Increasingly Difficult Questions as part of an eTextbook. A sample is available here and any feedback is absolutely welcome.

Anyway... Here are the sets of Increasingly Difficult Questions. I hope they're useful.

LEVEL 2 FURTHER MATHEMATICS

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In 2016, I attended #MathsConf7 in Leeds. The outcome? A to-do list longer than my arm as I intended to create a textbook of exercises of increasingly difficult questions to improve upon the standard...

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Maths Teaching Resources | Dr Austin Maths

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Dr Austin Maths is a free-to-use Maths teaching resources website, focussing on quality resources for KS4 IGCSE and GCSE Maths.

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Resourceaholic - free resources and ideas for teaching secondary school maths

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Some higher level challenge

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Unfortunately, my father Don Steward passed away from Covid-19 on 3rd May 2020.

Throughout his working life he was passionate about improving the teaching of mathematics and has requested that all of his work remains freely available.

As per his wishes, I have uploaded all of his work to this Blog in the pages section which contains links to google drive where slides and presentations can be downloaded for free.

Don has also requested that those who use his work make a discretionary donation to charities supporting education in Africa.

We have set up a Justgiving fundraising page to support this wish below:
https://www.justgiving.com/fundraising/jessesteward

Many thanks for all of the kind messages we have received which are of great comfort to myself and the family.

Kind regards,

Jess

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ideas and resources for mathematics teachers of 10 to 16 year olds

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Although manipulatives and representations are commonly used in primary mathematics or have been historically considered the reserve of lower prior attainers, they can be equally valuable for revealing mathematical structures at secondary level for all students.

We have produced guidance for some of the most useful representations for Key Stage 3 mathematics. Each guidance document details:

what they are

why they are important

how they might be used.

Click the following links to download the guidance documents.
Please note some of the links to NCETM content in the documents below may not work. You can quickly find where the links point using the search tool on this website. If you cannot find what you're looking for, contact info@ncetm.org.uk.

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Using mathematical representations at KS3

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Guidance for some of the most useful representations for Key Stage 3 mathematics.

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Go Teach Maths: Handcrafted Resources for Maths Teachers

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Homepage - Go Teach Maths: Handcrafted Resources for Maths Teachers

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Ready-to-use mathematics resources for Key Stage 3, Key Stage 4 and GCSE maths classes.

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Some lovely differentiated worksheets with good variety

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Maths for Primary and Secondary

Resources for students and teachers

Access hundreds of quizzes and other interactive activities that will help you enjoy and improve your maths whether you are at school or at home. There are thousands of carefully designed questions to improve maths knowledge and help develop fluency in important maths skills. These activities, developed for ks1 up to GCSE, have been helping students to better their target grades for more than ten years.

You can access the activities for free, but if you sign up for an account activities will be grouped together by topic and your scores for the interactive games and quizzes will be saved so that you can keep track of your progress.

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Popular with both teachers and students, the questions in these free maths resources are carefully crafted and include the answers. They are designed to help students to take the first steps in each topic, then strengthen and extend their knowledge and skills. The resources include revision questions for KS2 SATs and GCSE.

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Maths Venns is my collection of Venn Diagram activities covering many mathematical ideas. Students must think hard to find examples that meet different combinations of criteria in order to complete the diagram. Are some regions impossible to fill, or have students simply not found an example yet?

You can search for different topics using the Topics menus above, and you can find out more about Maths Venns on this page.

My 2020 book, Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom, goes into detail about making the most of these activities in the classroom. You can order the book from Amazon, John Catt, or wherever you get your books.

My 2023 book, Tips for Teachers: 400+ ideas to improve your teaching, details my most recent thoughts on using these sequences effectively. You can order the book from Amazon, John Catt, or wherever you get your books.

I have an online course store which offers low-cost, high-quality CPD on-demand. Each course contains short videos, resources, research, activities and questions to reflect upon. The courses most suited to the activities on the Maths Venns website are:

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Rich Venn Diagram maths activities from Craig Barton @mrbartonmaths

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UKMT Problem Solving Questions on Colmanweb

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Great maths enrichment material: individual UKMT Senior Challenge questions arranged by topic. Try single questions or sets arranged by topic.

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Exam Questions by topic, arranged in increasing difficulty

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AQA GCSE Maths (9-1) Revision | Worksheets | Past Papers | ExamQA

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Multi-step problems where pupils only do the last step for the first question, then the last two steps for the second question, etc, until ultimately pupils do a full question with no prompts.

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(Skip to the resources by clicking here)

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Each slide contains one topic but with 6 different types of questions hitting A01, A02 and A03

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Practice exam papers, video tutorials and revision checklists

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The GCSE Maths Tutor from YouTube | 100% Student Pass Rate

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Learn GCSE Maths the easy way! With YouTube's favourite tutor; The GCSE Maths Tutor AKA TGMT! With a 100% pass rate, my proven system will...

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Exam Questions by topic, Videos and Past Papers

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A-Level Maths: 1:1 Tuition & Free Resources | John Armstrong

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Online 1:1 A-Level Maths & Further Maths tutor with Easter revision courses, plus free notes, past papers and video lessons. Start improving your grade today.

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Activities that combine 2 topics, e.g. averages with surds

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The latest entries posted on Interwoven Maths

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A selection of similar looking problems but that require different methods, good for practicing method selection and identifying topics

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SSDD stands for Same Surface, Different Depth. They are a special set of problems that may look the same at first glance, but require different mathematical ideas to solve them.

SSDD Problems have become one of my key strategies to use with my students to help them become better problem solvers.

You can search for different topics using the tags on the right-hand side (or below if using a mobile device), and you can find out more about SSDD Problems on this page.

My books

I have written two books about my use of these types of activities.

My 2020 book, Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom, goes into detail about making the most of these activities in the classroom. You can order the book from Amazon, John Catt, or wherever you get your books.

My 2023 book, Tips for Teachers: 400+ ideas to improve your teaching, details my most recent thoughts on using SSDD Problems effectively. You can order the book from Amazon, John Catt, or wherever you get your books.

My online courses

I have an online course store which offers low-cost, high-quality CPD on-demand. Each course contains short videos, resources, research, activities and questions to reflect upon. The courses most suited to the questions on the SSDD Problems website are:

Supporting this website

I do not make any money from this website, so if you did want to support its future development - and hopefully learn more about the pedagogy underpinning these ideas - then I would be so grateful if you would consider:

Thanks so much for taking the time to read this - now go and enjoy the site!
Craig

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Same Surface, Different Deep Structure maths problems from Craig Barton @mrbartonmaths